Does this overheating issue only affect 1231's or do 1230's need some cooling too?

ACA1230s are not affected, because they are using PGA processors (the package with "pins down, through the board"). These dissipate heat a little better than the QFP package that is used on the ACA1231.

Cooling never hurts, so you're free to add some if you feel like it. However, it may be more effective to reduce voltage on your power supply: We found during our tests that 5.3V instead of 5.0V increases heat by far. Your thought should be "eliminate the source of the problem, not the effect" (if there's a problem at all).